There is an option to add one issue to multiple sprints. It is useful when an issue was not resolved on time or an issue was reopened in one of the next sprints.
But it seems that it's not possible to have an estimation and spent time for each sprint to properly display burndown chart and reports.
This post is just a proposal. A field might have a setting to split values for each sprint:
If this option is selected, then issue will have field for each sprint. Actual field value will be a sum of those values: